Abstract
In this paper we prove that under certain convexity and symmetry assumptions on a domain in the plane any positive solutionu, of Δu+λf(u)=0, in,D,u=0 on ∂D has only one interior critical point. This extends results of L. E. Payne [1].
Zusammenfassung
In dieser Arbeit wird gezeigt, dass unter gewissen Konvexitäts-und Symmetrievoraussetzungen jede positive Lösungu des Problems Δu+λf(u)=0, inD,u=0 auf ∂D (D ein ebenes Gebiet) nur einen einzigen inneren kritischen Punkt hat.
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Sperb, R.P. Extension of two theorems of Payne to some nonlinear Dirichlet problems. Journal of Applied Mathematics and Physics (ZAMP) 26, 721–726 (1975). https://doi.org/10.1007/BF01596076
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DOI: https://doi.org/10.1007/BF01596076